Simplify the following expression: $ a = 6 - \dfrac{3z - 9}{2z + 9} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2z + 9}{2z + 9}$ $ \dfrac{6}{1} \times \dfrac{2z + 9}{2z + 9} = \dfrac{12z + 54}{2z + 9} $ Therefore $ a = \dfrac{12z + 54}{2z + 9} - \dfrac{3z - 9}{2z + 9} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{12z + 54 - (3z - 9) }{2z + 9} $ Distribute the negative sign: $a = \dfrac{12z + 54 - 3z + 9}{2z + 9}$ $a = \dfrac{9z + 63}{2z + 9}$